Question

In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm then radius of the circle is

(a) 6 cm

(b) 9 cm

(c) 7.5 cm

(d) 8 cm

Answer 1

ANSWER:
(c) 7.5 cm
Let OA = OC = r cm.
Then OE = (r - 3) cm and AE=12AB=6cm
Now, in right ΔOAE, we have:
$O{A}^2=O{E}^2+A{E}^2$
⇒ $(r{)}^2=(r-3{)}^2+6^2$
⇒ $r^2=r^2+9-6r+36$
⇒ $6r=45$6r = 45
⇒ $r=\frac{45}{6}=7.5cm$
Hence, the required radius of the circle is 7.5 cm.